[开_91]数念珠问题再次改编(比较变态)

lg_cai

题目：有一个和尚，他有一串念珠，共七七49颗，都按1~49的顺序编号，他数念珠有个怪癖，比较变态，第1号开始数，数到第23颗珠子（即23号珠子）便从它开始拿23颗念珠（即23-45号）出来，接着又从46号珠子开始数，数到第22颗（即18号珠子）时也从它开始拿22颗念珠（即18-22、46-49、1-13号）出来，并把先拿出来的那些颗珠子（即23-45号珠子）放到该位置。接着又从14号珠子开始数。。。。。。如此循环，重复上面的做法后，最后取出的那个珠子的号码是多少？请大家编程帮他解决。
注意：规律是每次数的次数比上一次减1，取出念珠的颗数也比上一次减1，当次数减为0时停止，拿出来的珠子要放回到新的位置，放回后接下来数数要从该放回念珠之后开始。

规则挺复杂的，不知道说清没有，如果大家觉的这道题简单，下次再搞更变态的数法。

我的答案是5，不过我也不知道对不对

[此贴子已经被作者于2006-3-10 16:42:53编辑过]

sandyw

以下是引用lg_cai在2006-3-10 15:37:08的发言：

题目：有一个和尚，他有一串念珠，共七七49颗，都按1~49的顺序编号，他数念珠有个怪癖，比较变态，第1号开始数，数到第23颗珠子（即23号珠子）便从它开始拿23颗念珠（即23-45号）出来，接着又从46号珠子开始数，数到第22颗（即18号珠子）时也从它开始拿22颗念珠（即18-22、46-49、1-13号）出来，并把先拿出来的那些颗珠子（即23-45号珠子）放到该位置（是否指放回23－45这个位置？）。接着又从14号珠子开始数。。。。。。如此循环，重复上面的做法后，最后取出的那个珠子的号码是多少？请大家编程帮他解决。
注意：规律是每次数的次数比上一次减1，取出念珠的颗数也比上一次减1，当次数减为0时停止，拿出来的珠子要放回到新的位置，放回后接下来数数要从该放回念珠之后开始。（不好意思，偶没明白这句话的意思）

规则挺复杂的，不知道说清没有，如果大家觉的这道题简单，下次再搞更变态的数法。

我的答案是5，不过我也不知道对不对

northwolves

我算得也是5

Sub xxx()
Dim all As Integer, first As Integer, i As Integer, j As Integer
Dim btmonk As New Collection, temp As New Collection
For i = 1 To 49
btmonk.Add i
Next

'pprint btmonk

first = 23
For j = 1 To first - 1
btmonk.Add btmonk(1)
btmonk.Remove 1
Next

'pprint btmonk

For j = 1 To first
temp.Add btmonk(1)
btmonk.Remove 1
Next

'pprint btmonk

Do While first > 0

first = first - 1

For j = 1 To first - 1
btmonk.Add btmonk(1)
btmonk.Remove 1
Next

'pprint btmonk

For j = 1 To first
temp.Add btmonk(1)
btmonk.Remove 1

Next

'pprint btmonk

For j = 1 To first + 1
btmonk.Add temp(1)
temp.Remove 1
Next

'pprint btmonk

Loop
MsgBox btmonk(btmonk.Count)
End Sub
'Private Sub pprint(ByVal btmonk As Collection)
'Dim x As String, j As Integer
'For j = 1 To btmonk.Count
'x = x & "," & btmonk(j)
'Next
'Debug.Print Mid(x, 2)
'End Sub

northwolves

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49
23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22
46,47,48,49,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22
18,19,20,21,22,46,47,48,49,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17
14,15,16,17
14,15,16,17,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45
39,40,41,42,43,44,45,14,15,16,17,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38
33,34,35,36,37,38
33,34,35,36,37,38,18,19,20,21,22,46,47,48,49,1,2,3,4,5,6,7,8,9,10,11,12,13
5,6,7,8,9,10,11,12,13,33,34,35,36,37,38,18,19,20,21,22,46,47,48,49,1,2,3,4
46,47,48,49,1,2,3,4
46,47,48,49,1,2,3,4,39,40,41,42,43,44,45,14,15,16,17,23,24,25,26,27,28,29,30,31,32
17,23,24,25,26,27,28,29,30,31,32,46,47,48,49,1,2,3,4,39,40,41,42,43,44,45,14,15,16
39,40,41,42,43,44,45,14,15,16
39,40,41,42,43,44,45,14,15,16,5,6,7,8,9,10,11,12,13,33,34,35,36,37,38,18,19,20,21,22
12,13,33,34,35,36,37,38,18,19,20,21,22,39,40,41,42,43,44,45,14,15,16,5,6,7,8,9,10,11
44,45,14,15,16,5,6,7,8,9,10,11
44,45,14,15,16,5,6,7,8,9,10,11,17,23,24,25,26,27,28,29,30,31,32,46,47,48,49,1,2,3,4
26,27,28,29,30,31,32,46,47,48,49,1,2,3,4,44,45,14,15,16,5,6,7,8,9,10,11,17,23,24,25
14,15,16,5,6,7,8,9,10,11,17,23,24,25
14,15,16,5,6,7,8,9,10,11,17,23,24,25,12,13,33,34,35,36,37,38,18,19,20,21,22,39,40,41,42,43
13,33,34,35,36,37,38,18,19,20,21,22,39,40,41,42,43,14,15,16,5,6,7,8,9,10,11,17,23,24,25,12
43,14,15,16,5,6,7,8,9,10,11,17,23,24,25,12
43,14,15,16,5,6,7,8,9,10,11,17,23,24,25,12,26,27,28,29,30,31,32,46,47,48,49,1,2,3,4,44,45
25,12,26,27,28,29,30,31,32,46,47,48,49,1,2,3,4,44,45,43,14,15,16,5,6,7,8,9,10,11,17,23,24
3,4,44,45,43,14,15,16,5,6,7,8,9,10,11,17,23,24
3,4,44,45,43,14,15,16,5,6,7,8,9,10,11,17,23,24,13,33,34,35,36,37,38,18,19,20,21,22,39,40,41,42
10,11,17,23,24,13,33,34,35,36,37,38,18,19,20,21,22,39,40,41,42,3,4,44,45,43,14,15,16,5,6,7,8,9
20,21,22,39,40,41,42,3,4,44,45,43,14,15,16,5,6,7,8,9
20,21,22,39,40,41,42,3,4,44,45,43,14,15,16,5,6,7,8,9,25,12,26,27,28,29,30,31,32,46,47,48,49,1,2
14,15,16,5,6,7,8,9,25,12,26,27,28,29,30,31,32,46,47,48,49,1,2,20,21,22,39,40,41,42,3,4,44,45,43
29,30,31,32,46,47,48,49,1,2,20,21,22,39,40,41,42,3,4,44,45,43
29,30,31,32,46,47,48,49,1,2,20,21,22,39,40,41,42,3,4,44,45,43,10,11,17,23,24,13,33,34,35,36,37,38,18,19
21,22,39,40,41,42,3,4,44,45,43,10,11,17,23,24,13,33,34,35,36,37,38,18,19,29,30,31,32,46,47,48,49,1,2,20
11,17,23,24,13,33,34,35,36,37,38,18,19,29,30,31,32,46,47,48,49,1,2,20
11,17,23,24,13,33,34,35,36,37,38,18,19,29,30,31,32,46,47,48,49,1,2,20,14,15,16,5,6,7,8,9,25,12,26,27,28
38,18,19,29,30,31,32,46,47,48,49,1,2,20,14,15,16,5,6,7,8,9,25,12,26,27,28,11,17,23,24,13,33,34,35,36,37
1,2,20,14,15,16,5,6,7,8,9,25,12,26,27,28,11,17,23,24,13,33,34,35,36,37
1,2,20,14,15,16,5,6,7,8,9,25,12,26,27,28,11,17,23,24,13,33,34,35,36,37,21,22,39,40,41,42,3,4,44,45,43,10
8,9,25,12,26,27,28,11,17,23,24,13,33,34,35,36,37,21,22,39,40,41,42,3,4,44,45,43,10,1,2,20,14,15,16,5,6,7
24,13,33,34,35,36,37,21,22,39,40,41,42,3,4,44,45,43,10,1,2,20,14,15,16,5,6,7
24,13,33,34,35,36,37,21,22,39,40,41,42,3,4,44,45,43,10,1,2,20,14,15,16,5,6,7,38,18,19,29,30,31,32,46,47,48,49
22,39,40,41,42,3,4,44,45,43,10,1,2,20,14,15,16,5,6,7,38,18,19,29,30,31,32,46,47,48,49,24,13,33,34,35,36,37,21
43,10,1,2,20,14,15,16,5,6,7,38,18,19,29,30,31,32,46,47,48,49,24,13,33,34,35,36,37,21
43,10,1,2,20,14,15,16,5,6,7,38,18,19,29,30,31,32,46,47,48,49,24,13,33,34,35,36,37,21,8,9,25,12,26,27,28,11,17,23
16,5,6,7,38,18,19,29,30,31,32,46,47,48,49,24,13,33,34,35,36,37,21,8,9,25,12,26,27,28,11,17,23,43,10,1,2,20,14,15
30,31,32,46,47,48,49,24,13,33,34,35,36,37,21,8,9,25,12,26,27,28,11,17,23,43,10,1,2,20,14,15
30,31,32,46,47,48,49,24,13,33,34,35,36,37,21,8,9,25,12,26,27,28,11,17,23,43,10,1,2,20,14,15,22,39,40,41,42,3,4,44,45
49,24,13,33,34,35,36,37,21,8,9,25,12,26,27,28,11,17,23,43,10,1,2,20,14,15,22,39,40,41,42,3,4,44,45,30,31,32,46,47,48
37,21,8,9,25,12,26,27,28,11,17,23,43,10,1,2,20,14,15,22,39,40,41,42,3,4,44,45,30,31,32,46,47,48
37,21,8,9,25,12,26,27,28,11,17,23,43,10,1,2,20,14,15,22,39,40,41,42,3,4,44,45,30,31,32,46,47,48,16,5,6,7,38,18,19,29
12,26,27,28,11,17,23,43,10,1,2,20,14,15,22,39,40,41,42,3,4,44,45,30,31,32,46,47,48,16,5,6,7,38,18,19,29,37,21,8,9,25
23,43,10,1,2,20,14,15,22,39,40,41,42,3,4,44,45,30,31,32,46,47,48,16,5,6,7,38,18,19,29,37,21,8,9,25
23,43,10,1,2,20,14,15,22,39,40,41,42,3,4,44,45,30,31,32,46,47,48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36
2,20,14,15,22,39,40,41,42,3,4,44,45,30,31,32,46,47,48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1
39,40,41,42,3,4,44,45,30,31,32,46,47,48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1
39,40,41,42,3,4,44,45,30,31,32,46,47,48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17
42,3,4,44,45,30,31,32,46,47,48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41
45,30,31,32,46,47,48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41
45,30,31,32,46,47,48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22
31,32,46,47,48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30
47,48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30
47,48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30,42,3,4,44
48,16,5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30,42,3,4,44,47
5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30,42,3,4,44,47
5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30,42,3,4,44,47,31,32,46
5,6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30,42,3,4,44,47,31,32,46
6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30,42,3,4,44,47,31,32,46
6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30,42,3,4,44,47,31,32,46,48,16
6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30,42,3,4,44,47,31,32,46,48,16
6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30,42,3,4,44,47,31,32,46,48,16
6,7,38,18,19,29,37,21,8,9,25,49,24,13,33,34,35,36,23,43,10,1,12,26,27,28,11,17,39,40,41,2,20,14,15,22,45,30,42,3,4,44,47,31,32,46,48,16,5

清风_ll

不知道有没有理解错误,用数组方法答案是20

Option Explicit
Option Base 1
Dim PrayerBeads(), PreGetBeads()

Sub GetBead()
Dim sArrb
Dim i As Integer
ReDim PrayerBeads(1 To 26)
ReDim PreGetBeads(1 To 23)
sArrb = "46,47,48,49,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22"
sArrb = VBA.Split(sArrb, ",")

For i = 1 To 23
PreGetBeads(i) = i + 22
Next
For i = 0 To UBound(sArrb)
PrayerBeads(i + 1) = sArrb(i)
Next

Beads 22

End Sub

Sub Beads(iNum As Integer)

Dim i As Integer, j As Integer, k As Integer, tmpBeads(), iPos As Integer, iPos0 As Integer
'========================================================
'iNum=0时结束
If iNum = 0 Then MsgBox "最后取出的念珠号码为: " & PreGetBeads(1), vbOKOnly, "数念珠": Exit Sub

'========================================================
'将上次取出结果保存在tmpBeads数组中
tmpBeads = PreGetBeads

'定义本次取出的念珠数组
ReDim PreGetBeads(1 To iNum)
'=======================================================
'从n位开始取出念珠,并存入数组PreGetBeads,并将原念珠数组中相应位置号码置0
k = 0
For i = iNum To 2 * iNum - 1
If i > UBound(PrayerBeads) Then
k = k + 1
iPos = k
Else
iPos = i
End If
PreGetBeads(i - iNum + 1) = PrayerBeads(iPos)
PrayerBeads(iPos) = 0
Next
'==============================================
'取得剩余号码

Dim tmp()
ReDim tmp(1 To UBound(PrayerBeads) - iNum)
Debug.Print UBound(tmp)
k = 0: j = 0
For i = iPos + 1 To iPos + UBound(PrayerBeads)
If i > UBound(PrayerBeads) Then
k = k + 1
iPos0 = k
Else
iPos0 = i
End If

If PrayerBeads(iPos0) <> 0 Then
j = j + 1
tmp(j) = PrayerBeads(iPos0)
End If
Next

'===============================================
'生成新数组
PrayerBeads = tmpBeads
ReDim Preserve PrayerBeads(1 To 49 - iNum)
k = 0
For i = (UBound(tmpBeads) + 1) To UBound(PrayerBeads)
k = k + 1
PrayerBeads(i) = tmp(k)
Next

Beads iNum - 1

End Sub

lg_cai

以下是引用northwolves在2006-3-12 16:01:59的发言：

我算得也是5

Sub xxx()
Dim all As Integer, first As Integer, i As Integer, j As Integer
Dim btmonk As New Collection, temp As New Collection
For i = 1 To 49
btmonk.Add i
Next

'pprint btmonk

first = 23
For j = 1 To first - 1
btmonk.Add btmonk(1)
btmonk.Remove 1
Next

'pprint btmonk

For j = 1 To first
temp.Add btmonk(1)
btmonk.Remove 1
Next

'pprint btmonk

Do While first > 0

first = first - 1

For j = 1 To first - 1
btmonk.Add btmonk(1)
btmonk.Remove 1
Next

'pprint btmonk

For j = 1 To first
temp.Add btmonk(1)
btmonk.Remove 1

Next

'pprint btmonk

For j = 1 To first + 1
btmonk.Add temp(1)
temp.Remove 1
Next

'pprint btmonk

Loop
MsgBox btmonk(btmonk.Count)
End Sub
'Private Sub pprint(ByVal btmonk As Collection)
'Dim x As String, j As Integer
'For j = 1 To btmonk.Count
'x = x & "," & btmonk(j)
'Next
'Debug.Print Mid(x, 2)
'End Sub

正确，用Collection来解决倒是挺方便的，我用的是数组

lg_cai

以下是引用清风_ll在2006-3-12 23:40:46的发言：

不知道有没有理解错误,用数组方法答案是20

'生成新数组
PrayerBeads = tmpBeads
ReDim Preserve PrayerBeads(1 To 49 - iNum)
k = 0
For i = (UBound(tmpBeads) + 1) To UBound(PrayerBeads)
k = k + 1
PrayerBeads(i) = tmp(k)
Next

Beads iNum - 1

End Sub

谢谢清风兄参与，你的理解有一点问题，就是把念珠放回去后应该从它的后面接着数，而你的代码是从放回去的第一颗开始数。

我把最后几句改了一下

'===============================================
'生成新数组
ReDim Preserve PrayerBeads(1 To 49 - iNum)
For i = 1 To 49 - iNum
If i <= UBound(tmp) Then
PrayerBeads(i) = tmp(i)

Else
PrayerBeads(i) = tmpBeads(i - UBound(tmp))
End If
Next

Beads iNum - 1

清风_ll

原来是这个意思啊

lg_cai

我的解法

Sub cai()
Dim arr()
Dim i%, s1%, s2%, z1%, c1%, q1%, q2%
s1 = 49
s2 = 23
ReDim arr(0 To s1)

For i = 0 To s1 - 1
arr(i) = i + 1
Next i
arr(s1) = 1

Do While s2 > 0

For i = 1 To s2 - 1
z1 = arr(z1)
Next i
z2 = z1
q1 = arr(z1)

For i = 1 To s2
z1 = arr(z1)
Next i
q2 = z1

If c1 = 0 Then
arr(z2) = arr(z1)
Else
arr(c2) = arr(z1)
arr(z2) = c1

End If
c1 = q1
c2 = q2
s2 = s2 - 1
Loop
MsgBox "答案为 " & q1
End Sub

jsxjd

来个短的程序：
'字符串法
Sub getLastBead()
    n = 49: m = 23
    beads = "": removedBeads = ""
    For i = 1 To n: beads = beads & Format(i, "00"): Next
    startNo = 0
    For i = m To 1 Step -1
        NBs = Len(beads) / 2
        startNo = (startNo + i - 1) Mod NBs
        tempBeads = Right(beads, 2 * (NBs - startNo)) & Left(beads, 2 * startNo)
        beads = removedBeads & Right(tempBeads, 2 * (NBs - i))
        startNo = Len(removedBeads) / 2
        removedBeads = Left(tempBeads, 2 * i)
    Next
    Debug.Print Val(removedBeads)
End Sub